Question

In the given figure chord AB is congruent to chord CD, if arc(AB) = ${85}^{\circ }$ and arc(CD) = $(3k+55{)}^{\circ }$, then what is the value of $k$?

• A. 5
• B. 10
• C. 15
• D. 20

Answer 1

The correct option is B 10

As we know, If two chords of a circle are equal then their corresponding arcs are congruent.
Here, chord AB is congruent to chord CD.
$\Rightarrow$ arc(AB) = arc(CD)
$\Rightarrow$ ${85}^{\circ }=(3k+55{)}^{\circ }$
$\Rightarrow$ $85-55=3k$
$\Rightarrow$ $3k=30$
$\Rightarrow$ $k=10$
Hence, the value of $k$ is 10.